Tutz, Gerhard; Scholz, T.
Semiparametric Modelling of Multicategorical Data.
Collaborative Research Center 386, Discussion Paper 209
Parametric multicategorical models are an established tool in statistical data analysis. Alternative semi-parametric models are introduced where part of the explanatory variables is still linearly parametrized and the rest is given as a sum of unspecified functions of the explanatory variables. The modelling approach distinguishes between global and category specific variables, in contrast to global variables the latter may have different values for differing categories of the response. Estimation procedures are derived which make use of an expansion in basis functions which are localized on a grid of values of the explanatory variables. Regularization of the estimates is obtained by penalization.